where \(T_i f(y_1, \dots , y_i, \dots , y_N) := f(y_1, \dots , q y_i, \dots , y_N)\) . This is the \(0 < q=t < 1, r=1\)  version of the \(q, t\)  Macdonald difference operator \(D_N^r\)  defined in the scriptures [1]}. It has Schur functions as eigenfunctions:
\(D_q s_{\lambda }(Y) = \left( \sum _i q^{\lambda _i+N-i} \right) s_{\lambda } (Y).\) 
